Theorems · Theorem · general topology

upperHemicontinuous_iff_forall_isOpen

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f : α → Set β} [inst_1 : TopologicalSpace β],
  UpperHemicontinuous f ↔ ∀ (x : α) (u : Set β), IsOpen u → f x ⊆ u → ∀ᶠ (x' : α) in nhds x, f x' ⊆ u

Defined in

Mathlib.Topology.Semicontinuity.Hemicontinuity

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace